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MeganDarling
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A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use?
3 lbs peanuts, 6 lbs almonds, 2 lbs raisins
8 lbs peanuts, 1 lb almonds, 2 lbs raisins
6 lbs peanuts, 3 lbs almonds, 2 lbs raisins
8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
 2 years ago
 2 years ago
MeganDarling Group Title
A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is $21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins
 2 years ago
 2 years ago

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jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
Start off by defining variables
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
okey (:
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
That they add up to 11 pounds haha
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
good, so x y and z add to 11, which means x+y+z = 11
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
that's one equation
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
so x+y+z=11 :o
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
yes
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
But then we have to factor in how much they cost..
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
We also know that "The cost of peanuts is $1.50 per pound, almonds cost $3.00 per pound, and raisins cost $1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
this total cost is given to be $21 so 1.5x + 3y + 1.5z = 21
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
so like, 1.50x+3.00y+1.50=21..
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
Haha Okey you already said that x.x my bad
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
1.50z* I meant btw haha. I get that indeed.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
close, you mean to say 1.50x+3.00y+1.50z=21 but you got it
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
And don't forget twice the peanuts!
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
that's your 2nd equation
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
twice the peanuts as what?
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
it says, the recipe calls for twice as many peanuts as almonds O.o
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
good, so the equation for that is?
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
not quite
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
knew it was wrong x.x
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
Amount of peanuts = 2 times (amount of almonds)
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
y = 2 times x or just y = 2x
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
oh pshh I should have thought of that x.x
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
you can use them to solve for x, y and z
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
I'll get you started
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
Lol I can't because I'm stupid, But smart people definitely can haha
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
x+y+z = 11 x+2x+z = 11 3x+z = 11  1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
where are you lost?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
oh okay ! I see now, sorry it's really late and I'm super tired :/
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
so you have 3x+z = 11 7.5x + 1.5z = 21 now
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
solve the first equation for z to get this 3x+z = 11 3x+z  3x = 11  3x z = 11  3x
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
Alrighty
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
Since z = 11  3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11  3x) = 21 Solve for x
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
oh wait, i made a variable mistake...i switched x and y one sec
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
Let me fix real quick
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
I was thinking that haha x) ..
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
uhh ? your comment disappeared .. :o
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11  3y  1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11  3y) = 21 Solve that last equation for y
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
sry
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
Solve 6y + 1.5(11  3y) = 21 for y
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
haha it's okay
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
Aw man I have to go to bed soon I'm dead tired x.x
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
What do you get when you solve that equation for y
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
ergh I dunno x.x I'm brain dead
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.0
Then give it a break, get some sleep and you'll tackle it in the morning
 2 years ago

MeganDarling Group TitleBest ResponseYou've already chosen the best response.1
Oh no I keep losing connection >.<
 2 years ago
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